If A =[31−12],\text{If A }= \begin{bmatrix}[r] 3 & 1 \ -1 & 2 \end{bmatrix},If A =[3−112], then A2 =
[85−53]\begin{bmatrix}[r] 8 & 5 \ -5 & 3 \end{bmatrix}[8−553]
[8−553]\begin{bmatrix}[r] 8 & -5 \ 5 & 3 \end{bmatrix}[85−53]
[8−5−5−3]\begin{bmatrix}[r] 8 & -5 \ -5 & -3 \end{bmatrix}[8−5−5−3]
[8−5−53]\begin{bmatrix}[r] 8 & -5 \ -5 & 3 \end{bmatrix}[8−5−53]
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Given,
A=[31−12]⇒A2=[31−12][31−12]=[3×3+1×(−1)3×1+1×2(−1)×3+2×(−1)(−1)×1+2×2]=[9−13+2−3−2−1+4]=[85−53]∴A2=[85−53].\text{A} = \begin{bmatrix}[r] 3 & 1 \ -1 & 2 \end{bmatrix} \\[0.5em] \Rightarrow \text{A}^2 = \begin{bmatrix}[r] 3 & 1 \ -1 & 2 \end{bmatrix}\begin{bmatrix}[r] 3 & 1 \ -1 & 2 \end{bmatrix} \\[0.5em] = \begin{bmatrix}[r] 3 \times 3 + 1 \times (-1) & 3 \times 1 + 1 \times 2 \ (-1) \times 3 + 2 \times (-1) & (-1) \times 1 + 2 \times 2 \end{bmatrix} \\[0.5em] = \begin{bmatrix}[r] 9 - 1 & 3 + 2 \ -3 - 2 & -1 + 4 \end{bmatrix} \\[0.5em] = \begin{bmatrix}[r] 8 & 5 \ -5 & 3 \end{bmatrix} \\[0.5em] \therefore \text{A}^2 = \begin{bmatrix}[r] 8 & 5 \ -5 & 3 \end{bmatrix}.A=[3−112]⇒A2=[3−112][3−112]=[3×3+1×(−1)(−1)×3+2×(−1)3×1+1×2(−1)×1+2×2]=[9−1−3−23+2−1+4]=[8−553]∴A2=[8−553].
∴ Option 1 is the correct option.
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If A =[0010],\text{If A }= \begin{bmatrix}[r] 0 & 0 \ 1 & 0 \end{bmatrix},If A =[0100], then A2 =
If A =[1011],\text{If A }= \begin{bmatrix}[r] 1 & 0 \ 1 & 1 \end{bmatrix},If A =[1101], then A2 =
[2011]\begin{bmatrix}[r] 2 & 0 \ 1 & 1 \end{bmatrix}[2101]
[1012]\begin{bmatrix}[r] 1 & 0 \ 1 & 2 \end{bmatrix}[1102]
[1021]\begin{bmatrix}[r] 1 & 0 \ 2 & 1 \end{bmatrix}[1201]
none of these
If matrix 𝐴 = [2202] and A2=[4x04]\begin{bmatrix}[r] 2 & 2 \ 0 & 2 \end{bmatrix}\text{ and } A^2 = \begin{bmatrix}[r] 4 & x \ 0 & 4 \end{bmatrix}[2022] and A2=[40x4], then the value of x is :
2
4
8
10
If A = [2−2−22],\begin{bmatrix}[r] 2 & -2 \ -2 & 2 \end{bmatrix},[2−2−22], then A2 = pA, then the value of p is
-2
-4
